Watermelon is just starting to come in season in the northeastern U.S., and having a seedless watermelon is convenient. The only downside is, the "seedless" almost always still have the immature, sterile white seeds in them.

What is the mechanism for breeding these watermelons so that only these white seeds remain? What is the genotype that results? Could the genetics be modified so that there are virtually no seeds (short of any minor aberrations) left in the flesh of the fruit?